Open AccessSpherical Mexican hat wavelet: an application to detect non‐Gaussianity in the COBE ‐DMR maps
Author(s) -
Cayón L.,
Sanz J.L.,
MartínezGonzález E.,
Banday A.J.,
Argüeso F.,
Gallegos J.E.,
Górski K.M.,
Hinshaw G.
Publication year - 2001
Publication title -
monthly notices of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.058
H-Index - 383
eISSN - 1365-2966
pISSN - 0035-8711
DOI - 10.1111/j.1365-2966.2001.04641.x
Subject(s) - kurtosis , physics , skewness , wavelet , non gaussianity , cosmic microwave background , gaussian , maxima and minima , statistical physics , astrophysics , scale (ratio) , cosmic background radiation , cosmology , computational physics , statistics , optics , mathematics , mathematical analysis , anisotropy , quantum mechanics , artificial intelligence , computer science
The spherical Mexican hat wavelet is introduced in this paper, with the aim of testing the Gaussianity of the cosmic microwave background temperature fluctuations. Using the information given by the wavelet coefficients at several scales, we have performed several statistical tests on the COBE ‐DMR maps to search for evidence of non‐Gaussianity. Skewness, kurtosis, scale–scale correlations (for two and three scales) and Kolmogorov–Smirnov tests indicate that the COBE ‐DMR data are consistent with a Gaussian distribution. We have extended the analysis to compare temperature values provided by COBE ‐DMR data with distributions (obtained from Gaussian simulations) at each pixel and at each scale. The number of pixels with temperature values outside the 95 and 99 per cent limits is consistent with that obtained from Gaussian simulations, at all scales. Moreover, the extrema values for COBE ‐DMR data (maximum and minimum temperatures in the map) are also consistent with those obtained from Gaussian simulations.